Heat transfer apparatus



Dec. 22, 1959 H. s. ACKERMAN HEAT TRANSFER APPARATUS 6 Sheets-Sheet 1 Filed April 25, 1956 INVENTOR Harold fiAckzrman Dec. 22, 1959 H. s. ACKERMAN HEAT TRANSFER APPARATUS 6 Sheets-Sheet 2 Filed April 25, 1956 IN VEN TOR Harold S. Ackerma n.

EA 4M (AM/Z227.

A TTOP/VEYS Dec. 22, 1959 H. s. ACKERMAN HEAT TRANSFER APPARATUS 6 Sheets-Sheet 3 Filed April 25, 1956 INVENTOR. Harold S.Ackerman.

ZAM Mifi A 7'TOPNEY5 Dec. 22, 1959 H. s. ACKERMAN HEAT TRANSFER APPARATUS 6 Sheets-Sheet 4 Filed April 25, 1956 .0 m e k C V 5 mm JMM A 7'TOP/VE vs Des. 22, 1959 H. s. ACKERMAN 2,918,043

HEAT TRANSFER APPARATUS Filed April 25. 1956 s Sheets-Sheet s FIG? 3 LLI I. u 2

4 l- 8 5 5 m m 3-- I a 1. u.2-- o 5 1 X=DISTANCE "x"' .i9. 0 2' '4 6 6 lb i2 LENGTH OF PASSAGE (INCHES) FIG. 8

INVENTOR HAROLD S. ACKERMAN /flwuamfoal ATTORNEYS States This invention relates to heat transfer apparatus and particularly to a novel heat transfer passageway construction for effecting the exchange of heat between flowing fluids.

In general, the novel heat transfer passageway construction of the invention is particularly adaptable to a novel water heating apparatus described and illustrated herein and comprising an aspect of the present invention. Such water heating apparatus includes a heat transfer unit constructed of a plurality of individual sections each of which includes horizontally extending passage means for conducting a flow of colder fluid to be heated. The individual sections of the heat transfer unit are shaped and arranged in assembled relationship so as to form vertically extending passage means or flues for location above a heating source to receive a flow of hot gases therefrom. The upwardly flowing hot gases in the vertically extending passage means are thereby passed in heat exchange relationship with the flowing colder fluid in the horizontally extending passage means and serve to heat same in a highly efficient manner.

The present invention relates to the shape and positioning of the units forming the above mentioned horizontally and vertically extending passage means and to their means of support. In particular, a plurality of sections are each provided with a plurality of superimposed horizontally extending passages of a particular cross-sectional shape such that spaces and confronting side walls of adjacent sections are disposed in upwardly converging relationship to form the above mentioned vertically extending flue passages with cross-sectional areas that progressively decrease in the direction of flow of the rising hot gases from the heating source. Such progressive decrease in cross-sectional area is accomplished in proportion to the variation in absolute temperature of the rising hot gases whereby exceptionally high and uniform velocities of the gases along the heat absorbing surfaces are maintained. This novel construction prevents rifling of hot gases through the center of the vertically extending flue passages and hence the prevention of the formation of cooler low velocity layers of gas adjacent the heat absorbing surfaces with an accompanying loss of efliciency.

In addition to the above described progressive decrease in area of the vertically extending flue passages, such passages may be provided with a tortuous configuration and fins to obtain a maximum heat absorption to the heat transfer surfaces through increased wiping action of the hot gases over said surfaces. Hence maximum heat absorption is obtained with a minimum of resistance to flow of the hot gases with a resulting exceptionally high efficiency for the size and Weight of the apparatus.

It is therefore an object of the present invention to provide a novel heat transfer unit which incorporates maximum exposure of heat absorbing surfaces to a flow of hot fluid or a radiant flame to obtain maximum heat absorption per pound of material and hence maximum economy of fabrication and operation.

It is another object of the present invention to provide a novel heat transfer unit having heat absorbing surfaces which reduce the friction imposed on flowing fluid or flames contacting said surfaces whereby more heat absorption per unit area of surface and hence increased thermal efliciency are obtained.

It is another object of the present invention to provide a novel heat transfer unit that effects a uniform rate of flow of flame and hot gases over the heat absorbing surfaces of the unit to prevent stratification of gases and hence to maintain uniform sweeping action of flame and hot gases over the entire area of heat absorbing surfaces.

It is another object of the present invention to provide a novel heat transfer unit for receiving a flow of hot fluid which unit imposes a minimum restriction to such flow per unit of heat absorbed whereby maximum combustion efficiency is obtained.

It is another object of the present invention to provide a novel heat transfer unit for a water heater which incorporates horizontally extending water passages formed by laterally adjacent sections, said water passages being of a particular configuration to provide particularly shaped flue passages between said adjacent sections.

It is another object of the present invention to provide a novel heat transfer unit for a water heater which incorporates horizontally extending water passages and vertically extending flue passages, said flue passages being in heat transfer relationship with said water passages and provided with cross-sectional areas which progressively decrease in proportion to the absolute temperature of the hot gases flowing through said flue passages.

It is another object of the present invention to provide a novel heat transfer unit for a water heater which in corporates horizontally extending water passages and vertically extending flue passages, said flue passages being in heat transfer relationship with said water passages and of tortuous configuration to increase the wiping action of hot gases on heat absorbing surfaces of said flue passages.

It is another ob ect of the present invention to provide a heat transfer apparatus of the type described which includes right and left end sections and a plurality of identical intermediate sections, said sectional construction providing means for readily varying the capacity of the apparatus according to the number of intermediate sections that are incorporated in the assembly.

It is another object of the present invention to provide a heat transfer apparatus of the type described which includes a plurality of separate sections joined in side by side relationship to form passages for fluid flow both within and intermediate said sections, certain of said sections including integrally formed support for the assembly of joined sections whereby said passage-forming sections also constitute the supporting frame for the entire apparatus.

Further objects and advantages of the present invention will be apparent from the following description, reference being had to the accompanying drawings wherein preferred forms of embodiments of the invention are clearly shown.

In the drawing:

Figure 1 is a front elevational view of a motor heating apparatus constructed according to the present invention;

Figure 2 is a front sectional view of the apparatus of Figure 1 with the section being taken along a vertical plane through the center of the apparatus of Figure 1;

Figure 3 is a side sectional view of the apparatus of the preceding figures which illustrates in broken elevation the left section of the heat transfer unit of the apparatus;

Fi'gure4 isa diagrammatic view of a tortuous heat transfer passage" constructed according to the present invention and incorporated in the apparatus of Figures 1 through 3;

Figure 5 is a diagrammatic view of a simplified heat transfer passage constructed according to the present in-- vention;

Figure 6 is a graphical illustration including a typical curve defining the mathematical relationship between cross-sectional area and linear extent of a heat transfer passage constructed according to the present invention and exemplified in Figures 4 and 5;

Figure 7 is a diagrammatic view of an element of gas showing dimensions thereof used in deriving an equation for determining the configuration of the structure of the present invention; and

Figure 8 is a graphical plot of an equation used in determining the configuration of the structure of the present invention.

Referring to Figure l of the drawing, a water heating apparatus constructed according to the present invention, is" indicated generally at 20. The apparatus is viewed from the front and includes a plurality of sections assembled in side by side relationship to provide horizontally extending water passages in heat exchange relationship with the products of combustion from a burner assembly. Such assembly of sections includes a left section indicated generally at 24, a right section indicated generally at 25, and one or more intermediate sections indicated generally at 26. When more than one intermediate section is employed, to provide added capacity for theunit, the additional intermediate sections are identical to section 26, illustrated, whereby flexibility of capacity with a minimum number of production shapes is achieved.

The left and right sections 24 and 25 include integrally formed legs 27 provided with inwardly disposed shoulders 28 which support a bracket 29 for mounting a plurality of burners 30. A fuel supply line 32 leads from a source of fuel, not illustrated, through a pressure regulator 34 and diaphragm valve 35 and thence to burners Pressure regulator 34 and diaphragm valve are of conventional types well known to the art. As seen in'Figure 1, the left section 24 and the right section 25 are provided with flanges 37 through which is extended a belt 38 provided with a nut 39. It will be understood that when nut 39 is tightened, the three sections 24, 25, and 26 are clamped together with the legs 27 of the left and right sections providing support for the assembled apparatus.

As illustrated in Figure l, the assembled apparatus is provided with a casing 41 having removable cover 42. The casing 41 and cover 42 are shown in sections in Figure 1 for the purpose of illustrating the construction of the heat transfer unit housed therein.

Reference is next made to Figure 2 which is a front sectional view taken along a vertical plane through left section 24, right section 25, and intermediate section 26 of the heat transfer unit. Left section 24 includes a plurality of superimposed horizontally extending water passages 45, 46, and 47. These water passages are also illustrated in broken section in Figure 3. Similarly, right section 25 and intermediate section 26 are provided with superimposed water passages 49, 50, 51, 52, 53, and 54. As seen in Figure 2, a right wall 56 of left section 26 and the confronting wall 57 of intermediate section 26 form a tortuous flue passage 58 having a lower end intake 60 of greater cross-sectional area than an upper outlet end.61. In a like manner, a left wall 63 of right section 25 and. a confronting right wall 64 of intermediate section 26 form a second upwardly extending tortuous flue passage 65 having a lower intake end 66 of greater cross-sectional area than an upper outlet end 67. It will. be understood that the surfaces 56, 57, 63, and 64 are heat'absorbing surfaces and are therefore preferably provided with fins 69 to increase the area of heatab sorbing surface exposed to the hot gases passing upwardly through tortuous passages 58 and 65. To collect the-hot gases leaving the flue passages the upper ends of sections 24, 25, and 26 include outwardly disposed flanges 71 which removably support a flue collector 72 provided with a stack connection 73.

Reference is next made to Figure 3 which consists of an interior or right side view of left section 24. The view of Figure 3 is taken along a line 33 of Figure 2 whereby the inner surface 56 of left section 24 is seen in side elevation. The left section 24 includes a hollow side portion forming a vertically disposed passage 81 and a second hollow side portion 83 forming a vertically disposed passage 84. An intake connection 85 includes a threaded hole 86 communicating with passage 84 and an outlet connection 88 is provided with a threaded hole 89 communicating with "vertical passage 81.

As seen in Figure 1, when the individual sections 24, 25, and 26 are assembled the left section 24 is connected to intermediate section 26 by a nipple 91 with such nipple having outwardly tapered portions 92 fitted into confronting reamed ends of outlet holes 89 and 93. In a similar manner, a nipple 91 effects a sealed connection between the outlet holes of intermediate section 26 and right section 25. The lower ends of each of the sections have the inlet connections 85 joined by tapered nipples 91 in an identical manner.

With reference to Figure 1, the joined inlet connections 85 communicate with a source of Water supply by means of a pipe 96 and the joined outlet connections 88 communicate with a pipe 97 leading to a destination to which hot Water is to be supplied.

As seen in Figure 1, the ends of the sections form vertical cleanout slots 100 which are maintained closed during operation by cover plates 101 removably secured to the ends of the sections by wing nuts 102. Removablecover plates 101 allow for easy cleaning of the heat ab-- sorbing surfaces such as 63.

Reference is next made to Figure 4 which is a dia-- grammatic view of one of the heat transfer passageways 58 or 65 of Figure 2 with such passageway being indicated generally at 58-D in Figure 4. As seen in Figure 4, surface 57 of intermediate section 26 includes alternately disposed protrusions 105 and 106 and depressions 107 and 108. The opposing surface 56 of left section 24 includes alternately disposed protrusions 110, 111, 112, and depressions 113, 114. Such protrusions and grooves on the confronting surfaces of the adjacent sections 24 and 26 form the tortuous shape of the passageway. In addition to being tortuous, the cross-sectional area of passageway 58D progressively decreases from a lower intake opening 60 to an upper outlet opening 61. In the particular heating unit illustrated in the preceding figures, one cross-sectional dimension d remains a con-. stant but the other cross-sectional dimension w is progressively reduced upwardly due to the progressive convergence of the confronting surfaces 56 and 57. The area a of the elements of cross-sectional area, such as 126, are substantially proportional, at any location along the vertical dimension of the passageway to the absolute temperature of the hot gases passing upwardly therethrough. This novel passageway configuration is employed in order to obtain maximum heat absorption by increasing the wiping action of the hot gases over the absorbing surfaces56 and 57. Since Charles Law states that at constant pressure the volume of a gas is directly proportional to itsabsolute temperature, the use of a: passageway having cross-secional area whichprogressively decreases in proportion to absolute temperature provides an upward flow of hot gases along theabsorbing surfaces at an exceptionally high and uniform velocity through the constantly diminishing area. This prevents rifling of the hot gases'through .thercenter. of. the. passage way and the presence of cooler layersofgas: adjacent to: the heat transfer surfaces;with.anaccompanyingflossmf;

efficiency, as occurs with passageways of conventional configuration. As an ultimate result, the exceptionally high elficiency obtained by the passageway configuration of the present invention makes possible the construction of a heat transfer apparatus of much greater capacity for a given size or weight of the unit.

Reference is next made to Figure 5 which shows a simplified heat transfer passageway indicated generally at 120 with such passageway 120 being constructed according to the present invention. The passageways 58-D of Figure 4 and 120 of Figure 5 are similar in that the area a of the cross-sectional elements 125 and 126 in both instances decrease progressively along the linear dimension H in proportion to the absolute temperature t of the hot products of combustion passing upwardly through said passageways. The areas a of the passageways, at any distance 11 above the bases thereof, are arranged to be substantially equal to a specific mathematical value defined by the following equation:

a=area of passageway d: depth of passageway w=width of passageway h=distance from base of passageway c=a constant determined from the length of the passageway and the temperature range of hot gases through the passageway x=exponent denoting variation in rate of absorption of heat for various temperature differences between hot gases and the absorbing surfaces.

If the dimension d of the passageways 58-D and 120 is maintained constant, as is the case with the heating apparatus illustrated in Figures 1 through 3, then the above equation can be simplified as follows:

w=(h-c)'-" The equation w=(h--c)" is an empirical equation to represent the approximate dimensions and shape of the passageway which decreases exponentially as described and illustrated in subject application.

H==Height of the passageway (from base to top) and for the boilers shown in this application, H =2.4(l2").

w=width of the, passageway at any position h of height above its base, w =.328 at base (1%") and w =.131 /s") at top. =A constant determined from the height of the passageway H and the ratio of the absolute temperatures at its ends, to give g=%;=2.50 in this case, and 0:2.35

x=Exponent determined by rate of absorption at various temperatures. In this case the exponent is taken so that 12:13 to meet the requirement that the upward flow of gas through the passageway be at a uniform rateof flow.

t =Absolute temperature of the hot gas at entrance to the passageway, t =2500 F. (absolute).

t =Absolute temperature of the hot gas at the top exit from passageway, t =1O00 F. (absolute). See Figure 6 attached for table of values.

While the above empirical equation with the values given above allow determination of the value of w with respect to h, c, x, and t for determining the desired curve as accurately as necessary for practical cast iron boiler construction and as used on applicants boiler, the relationships between the various factors can be more accurately expressed by a more general equation h(t)=h(uo) +Dethe derivation of which, and its evaluation in and application to the boiler described herein follows:

Consider an element of gas, as shown in Figure 7, whose Length=l, a constant Width=w, a constant so that the Cross sectional area=A=lw=a constant, Height=h a function of time, and

Absolute temperature=T a function of time Assume all the sides of the element as perfectly insulated against heat flow except the bottom, where the rate of heat flow 2 d1 is dH KA 7= u) 0] where:

K is the thermal conductivity of the obstructing layer between the hot gas and the bottom surface s is the thickness of the obstructing layer A is the cross sectional area as above T the absolute temperature of the element, a function of time T the absolute temperature on the surface of the other side or bottom of the obstructing layer Now the amount of heat H in the element is given by where c is the specific heat of the gas 11 is the density, a function of time, and the other terms are defined above.

The pressure P of the gas will be assumed to remain where the constant B is determined by some known condition. When t=0 then 7 where kT rn k (oo) In-T.

k I h tT T.1= 1 l o) al (12 simplified by substituting from (8) and (11) and KA 1 (K 40 13 6M8 2 00 0) 68 e) obtained by substituting from (3) and (4) and letting a: K :9. constant Pan From the gas law PV=kT and T= and from (3) PA I ur m Then 25),. TUD- k (0) :ruflz T0 l e) k (00) and T o 2 m) Setting up the known temperature of the gas entering the'passageway T and the temperature on the surface of the other side of the bottom of the layer T we have T =2666 F. absolute (2206 F. temperature of entering gas) T =66O F. absolute (206 F. temperature of water filled iron) Let k q =a constant and substituting in (11) and (12) we obtain substituting (13), (16) and (17) in gives at h =666q+2000qe (18) Let Then from (16) Substituting 19) in (18) when h m =l we obtain Now if the gas is to pass along the passageway of constant width w at a constant velocity v then the height -h of the passageway will have to vary so that an ele- 8 ment-of .gas,'as it moves through the passageway and loses heat, will decrease in size through change inheight only.

Then if x is the distance along the passageway measured from the intake end of the passage, and v is the constant velocity, then x=vt or t= Substituting (21) in (20) gives 4 h =1+3e =1+3e-" (22) where b =a constant 1) p cs.4v

Let

T =ternperature of gas at the exit end of passage=1000' F. absolute (540 F.)

and

h =height of passageway at its outlet end Then 5 2mb. o (m) and T 1000 f (w) 0n When 2:: w then Substituting (24) in (22) we get bx=log 6: 1.79176 (25) Now the ratio between the length and height of the passageway at its intake end is Plotting these values of ,1 we obtain the curve shown in Figure 8.

While the above equation does not include the additional heat absorbed by radiation from the radiant flame immediately above the burners, the major portion of this is absorbed by the lower extremities of thesections which guide the 1 0F8 0 into the entrance of the passageway described above and so have very little effect on the shape and dimensions of the passageway as defined by the above equation.

With reference to Figure 6, which is a typical graphical illustration of the above equation, it is seen that a plot of the various widths w relative to various distances from passageway entrance (height h above entrance 60 of straight passageway 120) constitutes a series of progressively increasing height and decreasing width values 122 which values define a curve indicated at 123.

It will now be understood from Figures and 6 that progressing along the length of a passageway of the invention, each element 125 of cross-sectional area is of a progressively decreasing width w with such decrease being produced in accordance with the width vs. distance from entrance values defined by curve 123. With reference to Figure 4, and tortuous passageway 58-D, each element of area 126, progressing lengthwise along the passage from entrance 60, is of a progressively decreasing width w, and such width vs. distance from entrance relationship is determined according to the equation set forth above and can be graphically represented by a particular curve similar to curve 123 shown in Figure 6.

The tortuous passageway 58-D is similar to that of simplified passageway 120 in that the cross-sectional areas of both passageways are each progressively de creased in proportion to the absolute temperatures existing along their linear extent. Such decrease is effected, in each case, according to the mathematical relationship defined by the above mentioned equation and graphically illustrated in Figure 6. The passageways differ, however, in that passageway 58-D, the diagrammatic representation of the passageways 58 and 65 of the apparatus of Figures 1 through 3, is made tortuous to provide a more effective wiping action by the upwardly moving products of combustion along the heat transfer surfaces contacted by such products. For purposes of simplification of illustration and description, the fins 69 of Figure 2 are omitted from the diagrammatical illustrations of Figures 4 and 5, it being understood that such fins can be incorporated to effect an increase in the heat transfer area contacted by the rising products of combustion.

It will further be understood that for purposes of simplicity the passageways utilized in the apparatus of Figures 1 through 3, and the passageways diagrammatically illustrated in Figures 4 and 5, are shown with a constant dimension d for one of the dimensions of the area elements 125 or 126. Hence the area a of such elements will vary in proportion to the width w and the above described simplified equation w=(hc)* will apply. The abscissa of the graph of Figure 6 will therefore represent a width value, as indicated by the notation w appearing thereon. It will be understood that if desired, both the dimensions w and d can be varied in various ways such that the area a of area element 125 or 126 will still vary according to the absolute temperature of the rising gases. In such instance the relationship of the area a relative to the distance from entrance I: is defined by the above described equation- In connection with the consideration of Figures 4 through 6, it should be mentioned that t1 denotes the absolute temperature of hot gas at the entrances 60 of a passageway and r-2 denotes the absolute temperature of hot gas at the exit 61 of a passageway. The constant c is determined from H, the total length of passageway, and the ratio of the absolute temperatures t] to t-2. The symbol w is used to denote one of the cross-sectional dimensions with the symbol d denoting the other cross-sectional dimension. In the simplified equation, mentioned above, w represents the variable cross-sectional dimension where the other cross-sectional dimension is a constant.

In operation of the apparatus of Figures 1 through 3, cold water from a water supply enters intake connection through pipe 96. The water then passes through horizontal passageways 45, 46, 47, 49, 50, 51, 52, 53, and 54, and vertical passageways 81 and 84 to the outlet connection 88. The path of flow of water through the units is diagrammatically illustrated by the flow arrows in Figure 3. In the course of passing through such horizontal passageway, the water is heated by heat transfer through surfaces 56, 57, 63, and 64 which surfaces are continuously wiped by the rising hot products of combustion from burners 30. As the rising hot products of combustion give up heat to the heat transfer surfaces, the rising gases will cool and, as previously described herein, the cross-sectional area of the passages 58 and 65 are decreased according to the absolute temperature of the gas at any point along the path of travel thereof. With such converging passage construction, the velocity of the rising gas is maintained at a high rate across the entire cross-sectional area of the passages. Hence the formation of stagnation areas along the heat transfer surfaces is completely avoided. In combination with the achieving of exceptionally high uniform velocities through constantly diminishing passage area, the passages are made tortuous and provided with fin 69 to obtain the maximum heat absorption and to increase wiping action of the hot gases on the heat absorbing surfaces. At the same time a minimum resistance to the flow of hot gases is achieved.

While the forms of embodiments of the present invention as herein disclosed constitute preferred forms, it

is to be understood that other forms might be adopted, all coming within the scope of the claims which follow:

I claim:

1. A heat transfer apparatus for the transfer of thermal energy from a flowing fluid to a substance to be heated, said apparatus comprising means forming a passageway for receiving said flow and converging in the direction of said flow at a rate proportional to the absolute temperatures of said flow along said passageway such that the decreasing cross-sectional area of the passageway, at any distance along said flow from a base, is defined by the equation:

a=area of passageway d=depth of passageway w=width of passageway h=distance from base of passageway c=a constant determined from the length of the passageway and the temperature range of hot gases through the passageway x=exponent denoting variation in rate of absorption of heat for various temperature differences between hot gases and the absorbing surfaces.

2. A heat transfer apparatus for the transfer of thermal energy from a flowing fluid to a substance to be heated, said apparatus comprising means forming a passageway for receiving said flow, said passageway being tortuous and converging in the direction of said flow at a rate proportional to the absolute temperatures of said flow along said passageway such that the decreasing cross-sectional area of the passageway, at any distance along said flow from a base, is defined by the equation:

a=area of passageway d=depth of passageway w=width of passageway h=distance from base of passageway 3. A water heater comprising, in combination, a right end section; a left end section; at least one intermediate section; upright conduit means for each of said sections;

transverse tubes in each of said sections for connecting said upright conduit means thereof, the confronting side walls of tubes of adjacent sections forming the confines 'of a-vertically extending passageway; heating meansbelow said passageway for providing -a flow'of hot gases upwardly therethrough, at least a portion of said passageway being convergent upwardly such that the decreasing cross-sectional area thereof,-at any distance along said flow from a base, is defined by the equation:

'wh'ere:

a=area of passageway 'd=depth of passageway w=width of passageway h=distance from base of passageway c=a constant determined from the length of the passageway and the temperature range of hot gases through the passageway x=exponent denoting variation in rate of absorption of heat for various temperature differences between hot gases and the absorbing surfaces.

substantially constant cross-sectional dimension and a second variable cross-sectional dimension that decreases along the passageway at a rate defined by the equation: w=(h=c)" where:

w=the variable cross-sectional dimension of passageway h=distance from base of passageway c=a constant determined from the length of the passageway and the temperature range of hot gases through the passageway x=exponent denoting variation in rate of absorption of heat for various temperature differences between hot gases and the absorbing surfaces.

5. Apparatus defined in claim 3 characterized by the cross-sectional shape of said passageway including a first substantially constant cross-sectional dimension and a second variable cross-sectional dimension that decreases along the passageway at a rate defined by the equation:

where:

w=the variable cross-sectional dimension of passageway h=distance from base of passageway c=a constant determined from the length of the passageway and the temperature range of hot gases through the passageway x:exponent denoting variation in rate of absorption of heat for various temperature dificrences between hot gases and the absorbing surfaces.

References Cited in the file of this patent UNITED STATES PATENTS 1,679,120 Fox July 31, 1928 1,247,796 Ackerman July 1, 1941 2,506,120 Turner May 2, 1950 

